Properties of Starless and Prestellar Cores in Taurus Revealed by Herschel SPIRE/PACS Imaging

0.51 MB·

by  K. A. Marsh

Mon.Not.R.Astron.Soc.000,1–12(2002) Printed31January2014 (MNLATEXstylefilev2.2)
Properties of Starless and Prestellar Cores in Taurus
⋆
Revealed by Herschel SPIRE/PACS Imaging
4
1 K. A. Marsh1†, M. J. Griffin1, P. Palmeirim2, Ph. Andr´e2, J. Kirk3,
0 D. Stamatellos3, D. Ward-Thompson3, A. Roy2, S. Bontemps4,5, J. Di Francesco6,
2
D. Elia7, T. Hill8, V. Ko¨nyves2,9, F. Motte2, Q. Nguyen-Luong10, N. Peretto1,
n
a S. Pezzuto7, A. Rivera-Ingraham11,12, N. Schneider4,5, L. Spinoglio7, and G. White13,14
J
0 1School of Physics and Astronomy, Cardiff University,Cardiff CF24 3AA, UK
3 2Laboratoire AIM, CEA/DSM-CNRS-Universit´e Paris Diderot, IRFU / Service d’Astrophysique, C.E. Saclay, Orme des Merisiers,
91191 Gif-sur-Yvette,France
] 3Jeremiah Horrocks Institute for Astrophysics and Supercomputing, Universityof Central Lancashire, Preston, PR1 2HE, UK
A 4Univ. Bordeaux, LAB, UMR 5804, 33270, Floirac, France
5CNRS, LAB, UMR 5804, 33270, Floirac, France
G
6National Research Council of Canada, Hertzberg Institute of Astrophysics, 5071 West Saanich Rd., Victoria, BC, V9E 2E7, Canada
. 7Istituto di Astrofisica e Planetologia Spaziali - INAF, ViaFosso del Cavaliere 100, I-00133 Roma Italy
h
8Joint ALMA Observatory, Alonso de Cordova, 3107, Vitacura, Santiago, Chile
p
9Institut d’Astrophysique Spatiale, UMR8617, CNRS/Universit´e Paris-Sud 11,91405 Orsay, France
-
o 10Department of Astronomy & Astrophysics, University of Toronto, 50 George Street, Toronto, ON M5S 3H4, Canada
r 11Universit´e de Toulouse, UPS-OMP, IRAP, Toulouse, France
st 12CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France
a 13Department of Physics and Astronomy, The OpenUniversity, Walton Hall, Milton Keynes,MK7 6AA, UK
[ 14RALSpace, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0NL, UK

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1 31January2014
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7 ABSTRACT
. ThedensityandtemperaturestructuresofdensecoresintheL1495cloudoftheTaurus
1
star-forming region are investigated using Herschel SPIRE and PACS images in the
0
70µm,160µm,250µm,350µmand500µmcontinuumbands.Asampleconsistingof
4
20cores,selectedusingspectralandspatialcriteria,isanalysedusinganewmaximum
1
: likelihood technique, COREFIT, which takes full account of the instrumental point
v
spread functions. We obtain central dust temperatures, T , in the range 6–12 K and
0
i
X find that, in the majority of cases, the radial density falloff at large radial distances
is consistent with the asymptotic r−2 variation expected for Bonnor-Ebert spheres.
r
a Two of our cores exhibit a significantly steeper falloff, however, and since both ap-
peartobegravitationallyunstable,suchbehaviourmayhaveimplicationsforcollapse
models. We find a strong negative correlation between T and peak column density,
0
as expected if the dust is heated predominantly by the interstellar radiation field. At
the temperatures we estimate for the core centres, carbon-bearing molecules freeze
out as ice mantles on dust grains, and this behaviour is supported here by the lack
of correspondence between our estimated core locations and the previously-published
positionsofH13CO+ peaks.Onthisbasis,ourobservationssuggestasublimation-zone
radiustypically∼104 AU.Comparisonwithpreviously-publishedN H+ dataat8400
2
AU resolution, however, shows no evidence for N H+ depletion at that resolution.
2
Key words: stars: formation — stars: protostars — ISM: clouds — submillimetre:
ISM — methods: data analysis — techniques: high angular resolution.
1 INTRODUCTION
⋆ Herschel isanESAspaceobservatorywithscienceinstruments
A key step in the star formation process is
provided by European-led Principal Investigator consortia and
the production of cold dense cores of molecu-
withimportantparticipationfromNASA.
† E-mail:[email protected] lar gas and dust (Ward-Thompson et al. 1994;
2 K. A. Marsh et al.
Andr´e,Ward-Thompson & Motte 1996). Cores which structuresisachievedusingournewly developedtechnique,
donotcontainastellarobjectarereferredtoasstarless;an COREFIT, complementary in some ways to the recently
important subset of these consists of prestellar cores, i.e., used Abel transform method (Royet al. 2013). Before dis-
those cores which are gravitationally-bound and therefore cussingCOREFITanditsresultsindetail,wefirstdescribe
present the initial conditions for protostellar collapse. ourobservations and core selection criteria.
Observations of cold cores are best made in the sub-
millimetre regime in which they produce their peak emis-
sion, and observations made with ground-based telescopes
2 OBSERVATIONS
havepreviouslyhelpedtoestablishimportantlinksbetween
the stellar initial mass function (IMF) and the core mass Theobservationaldataforthisstudyconsistsofasetofim-
function (CMF) (Motte, Andr´e& Neri1998).With thead- ages of the L1495 cloud in the Taurus star-forming region,
ventofHerschel (Pilbratt et al. 2010),however,thesecores made on 12 February, 2010 and 7–8 August, 2010, during
cannowbeprobedwithhigh-sensitivitymultibandimaging thecourseoftheHerschel GouldBeltSurvey(HGBS).The
in the far infrared and submillimetre, and hence the CMF data were taken using PACS (Poglitsch et al. 2010) at 70
can beprobed to lower masses than before. Oneof thema- µmand160µmandSPIRE(Griffin et al.2010)at250µm,
jor goals of the Herschel Gould Belt Survey (Andr´eet al. 350 µm, and 500 µm in fast-scanning (60 arcsec/s) paral-
2010) is to characterise the CMF over the densest portions lel mode. The Herschel Observation IDs were 1342202254,
of the Gould Belt. This survey covers 15 nearby molecu- 1342190616, and1342202090. Anadditional PACSobserva-
lar clouds which span a wide range of star formation en- tion (ID 1342242047) was taken on 20 March 2012 to fill a
vironments; preliminary results for Aquila have been re- datagap.Calibratedscan-mapimageswereproducedinthe
portedbyK¨onyveset al.(2010).AnotherHerschel keypro- HIPE Version 8.1 pipeline (Ott 2010) using the Scanamor-
gramme, HOBYS (“Herschel imaging survey of OB Young phos (Roussel 2013) and “naive” map-making procedures
Stellarobjects”) (Motte et al.2010),isaimed atmoremas- for PACS and SPIRE, respectively. A detailed description
sivedensecoresandtheinitialconditionsforhigh-massstar of theobservational and data reduction procedures is given
formation, and preliminary results have been presented by in Kirk et al. (2013).
Giannini et al. (2012).
The Taurus Molecular Cloud is a nearby region of pre-
dominantly non-clustered low-mass star formation, at an
3 CANDIDATE CORE SELECTION
estimated distance of 140 pc (Elias 1978), in which the
stellar density is relatively low and objects can be stud- The first step in our core selection procedure con-
iedinrelativeisolation.ItsdetailedmorphologyatHerschel sists of source extraction via the getsources algorithm1
wavelengths is discussed by Kirk et al. (2013). The region (Men’shchikov et al.2012)whichusestheimagesatallavail-
is dominated by two long (∼ 3◦), roughly parallel filamen- ablewavelengthssimultaneously.Theseconsistoftheimages
tarystructures,thelargerofwhichisthenorthernstructure. atallfiveHerschel bandsplusacolumndensitymapwhich
EarlyresultsfromHerschel regardingthefilamentaryprop- is used as if it were a sixth band,the purposebeing to give
erties havebeen reported byPalmeirim et al. (2013). extra weight to regions of high column density in the de-
Inthispaperwefocusonthestarlesscorepopulationof tection process. The column density map itself is obtained
the field with particular interest in core structure and star- from the same set of SPIRE/PACS images, using the pro-
forming potential. Our analysis is based on observations of ceduredescribed byPalmeirim et al. (2013) which provides
the western portion of the northern filamentary structure, a spatial resolution corresponding to that of the 250 µm
designated as N3 in Kirk et al. (2013), which includes the observations.
Lynds cloud L1495 and contains Barnard clouds B211 and The detection list is first filtered to remove unreliable
B213 as prominent subsections of the filament. Our anal- sources.Thisisbasedonthevalueofthe“globalgoodness”
ysis involves a sample of 20 cores which we believe to be parameter (Men’shchikov et al. 2012) which is a combina-
representativeofrelativelyisolatedcoresinthisregion.The tion of various quality metrics. It incorporates the quadra-
principal aims of thestudy are as follows: turesumsofboththe“detectionsignificance” andsignalto
noiseratio(S/N)overthesetofwavebands,aswellassome
(i) accuratemassestimation basedonmodelswhichtake
contrast-based information. The “detection significance” is
accountofradialtemperaturevariationsandwhichusespa-
defined with respect to a spatially bandpass-filtered image,
tial and spectral data;
thecharacteristic spatial scale of which matchesthatof the
(ii) a comparison of these results with those from sim-
source itself. At a given band, the detection significance is
plertechniquescommonlyusedforestimatingthecoremass
thenequaltotheratioof peak sourceintensity tothestan-
functioninordertoprovideacalibrationbenchmarkforsuch
darddeviation ofbackground noisein thisimage. TheS/N
techniques;
is defined in a similar way, except that it is based on the
(iii) investigationofprocessessuchasheatingofthedust
observed,rather than filtered, image.
by the interstellar radiation field (ISRF) and the effect of
For present purposes we require a “global goodness”
temperature gradients on core stability;
value greater than or equal to 1. A source satisfying this
(iv) examination of the results in the context of other
criterion may be regarded as having an overall confidence
observations of the same cores where possible, particularly
level>7σandcanthereforebetreatedasarobustdetection.
withregard togaining insightintotherelationship between
thedust and gas.
The estimation of the core density and temperature 1 Version1.130401wasusedfortheanalysisdescribedhere
Properties of Starless and Prestellar Cores in Taurus 3
Classification as a core for the purpose of this study then
involvesthe following additional criteria:
(i) detection significance (as defined above) greater than
or equal to 5.0 in thecolumn density map;
(ii) detection significance greater than or equal to 5.0 in
at least two wavebands between 160 µm and 500 µm;
(iii) detection significance less than 5.0 for the 70 µm
bandandnovisiblesignatureon the70 µmimage, inorder
toexcludeprotostellar cores, i.e., thosecores which contain
a protostellar object;
(iv) ellipticity less than 2.0, as measured by getsources;
(v) source not spatially coincident with a known galaxy,
based on comparison with the NASA Extragalactic
Database.
This procedure resulted in a total of 496 cores over
the observed 2◦.2 × 2◦.2 region. The total mass, 88 M⊙,
of the detected cores represents approximately 4% of the
mass of the L1495 cloud, estimated to be 1500–2700 M⊙
(Kramer & Winnewisser1991).Fromthisset,20coreswere
selected for detailed study. The main goal of the final se- Figure 1.SPIRE250µmimageoftheL1495region.Thegreen
circlesrepresentthelocations ofthe20cores selectedformodel-
lection process was to obtain a list of relatively uncon-
ing.Theother symbolsrepresentpreviouslypublishedcoreloca-
fused cores, uniformly sampled in mass according to pre-
tions at other wavelengths; red squares: H13CO+ (Onishietal.
liminary estimates obtained via SED fitting as outlined in
2002);bluetriangles:N2H+(Hacar etal.2013);yellowcross:850
thenext section. Cores which were multiply peaked or con-
µm(Sadavoy etal.2010).Theimageisshownonatruncatedin-
fused, based on visual examination of the 250–500 µm im- tensity scale in order to emphasize faint structure; the display
ages,wereexcluded.Themassrange0.02–2.0 M⊙ wasthen saturates at 200 MJy sr−1 which corresponds to 100% on the
divided into seven bins, each of which spanned a factor of greyscale.
twoinmass,andasmallnumberofobjects(nominallythree)
selectedfromeachbin.Theselectionwasmadeonarandom
basisexceptforapreferenceforobjectsforwhichpreviously- The models are based on spherical geometry, in which the
published data were available, thus facilitating comparison radialvariationsofvolumedensityandtemperaturearerep-
of deducedparameters. Fig. 1shows thelocations of the20 resented by parametrized functional forms. For a given set
selected cores on a SPIRE250 µm image of thefield. of parameters, a model image is generated at each of the
five wavelengths by calculating the emergent intensity dis-
tributionontheplaneoftheskyandconvolvingitwith the
4 SED FITTING instrumentalpointspreadfunction(PSF)2 attheparticular
wavelength.Theparametersare thenadjustedtoobtain an
Preliminaryvaluesofcoremassesanddusttemperaturesare inverse-variance weighted least squares fit to the observed
estimated by fitting a greybody spectrum to the observed images.
spectralenergydistribution(SED)constructedfromtheset
Inthisprocedurethewavelengthvariationofopacityis
of five-wavelength getsources fluxes. For this computation, assumedtobegivenbyEq.(1)andthetheradialvariations
sourcesareassumedtobeisothermalandhaveawavelength of volume density and dust temperature are assumed to be
variationofopacityoftheform(Hildebrand1983;Roy et al.
described by Plummer-like (Plummer 1911) and quadratic
2013): forms, respectively. Specifically we use:
κ(λ)=0.1(300/λ[µm])2 cm2g−1 (1) n(r) = n /[1+(r/r )α] (2)
0 0
Although obtained observationally, the numerical value of T(r) = T +(T −T −T )r/r +T (r/r )2 (3)
0 1 0 2 out 2 out
the coefficient in this relation is consistent with a gas to
where n(r) represents the number density of H molecules
dust ratio of 100. 2
at radial distance r, r represents the radius of an inner
0
plateau, and r is the outer radius of the core, outside of
out
which the core density is assumed to be zero. Also, T is
0
5 CORE PROFILING
the central core temperature, T is the temperature at the
1
Toobtainbetterestimatesofcoremassandotherproperties, outer radius, and T2 is a coefficient which determines the
curvatureof theradial temperature profile.In relating n(r)
a more detailed model fit is required. For this purpose we
havedevelopedanewprocedure,COREFIT,whichinvolves
maximumlikelihoodestimationusingbothspatialandspec-
tral information. 2 ForthePACSimages,weuseazimuthally-averagedversionsof
The fitting process involves calculating a series of for- the PSFs estimated from observations of Vesta (Lutz 2012); for
ward models, i.e., sets of model images based on assumed SPIRE we use rotationally symmetric PSFs based on the mea-
parameter values, which are then compared with the data. suredradialprofilespresentedbyGriffinetal.(2013).
4 K. A. Marsh et al.
to the corresponding profile of mass density we assume a obtainedbyintegratingthedensityprofilegivenbyEq.(2),
mean molecular weight of 2.8 (Roy et al. 2013). evaluated using theestimated valuesof n , r and α.
0 0
The set of unknowns then consists of: n , r , r , α, Evaluation of the uncertainties in parameter estimates
0 0 out
T ,T ,T ,x,y,wherethelattertwovariablesrepresentthe iscomplicatedbythenonlinearnatureoftheproblemwhich
0 1 2
angularcoordinatesofthecorecentre.Representingthisset leads to a multiple-valley nature of φ(p). The usual proce-
by an 9-component parameter vector, p, we can write the dure, in which the uncertainty is evaluated by inverting a
measurement model as: matrix of 2ndderivativesof φ(p)(Whalen 1971),thenonly
providesvalueswhichcorrespondtothewidthoftheglobal
ζ =f (p)+b +ν (4)
λ λ λ λ maximum and ignores the existence of neighbouring peaks
whereζ isavectorrepresentingthesetofpixelsoftheob- which may represent significant probabilities. We therefore
λ
served image at wavelength λ, f (p) represents the model evaluate the uncertainties using a Monte Carlo technique
λ
core image for parameter set p, and ν is the measure- in which we repeat theestimation procedureafter addinga
λ
mentnoisevector,assumedtobeanuncorrelatedzero-mean series of samples of random noise to the observational data
Gaussianrandomprocess.Also,b representsthelocalback- and examine theeffect on theestimated parameters.
λ
ground level, estimated using the histogram of pixel values WehavealsoimplementedanalternateversionofCOR-
in an annulus3 surrounding the source. This measurement EFIT, referred to as “COREFIT-PH,” in which the dust
model assumes implicitly that the core is optically thin at temperature profile is based on a radiative transfer model,
all wavelengths of observation. PHAETHON(Stamatellos & Whitworth2003),ratherthan
Inprinciple,thesolution procedureisthentominimise estimating it from the observations. In this model, the ra-
thechi squared function, φ(p), given by: dial density profile has the same form as for the standard
COREFIT (Eq. (2)) but with the index, α, fixed at 2. The
φ(p)=X[(ζλ)i−bλ−(fλ(p))i]2/σλ2 (5) temperature profile is assumed to be determined entirely
by the heating of dust by the external ISRF; the latter is
λ,i
modeled locally as a scaled version of the standard ISRF
where subscript i refers to the ith pixel of the image at the
(Stamatellos, Whitworth & Ward-Thompson 2007) using a
given wavelength and σ represents the standard deviation
λ scalingfactor,χ ,whichrepresentsanadditionalvariable
ISRF
of the measurement errors, evaluated from the sky back-
in the maximum likelihood solution.
ground fluctuations in the background annulus.
We now compare the results obtained using the two
In practice, two difficulties arise: approaches, both for syntheticand real data.
(i) Anunconstrainedminimisationofφ(p)isnumerically
unstable due to the fact that for a given total number of 5.1 Tests with synthetic data
molecules, n in Eq. (2) becomes infinite as r → 0. It re-
0 0
WehavetestedbothCOREFITandCOREFIT-PHagainst
sults in near-degeneracy such that the data do not serve to
synthetic data generated using an alternate forward model
distinguish between a large range of possible values of the
fordustradiativetransfer,namelyMODUST(Bouwmanet
centraldensity.Toovercomethis,wehavemodifiedthepro-
al.,inpreparation).Usingthelattercode,imagesatthefive
cedure to incorporate the constraint r > r , where r
0 min min
wavelengthsweregeneratedforasetofmodelcoresandcon-
is equal to one quarter of the nominal angular resolution,
volvedwithGaussiansimulatedPSFswithfullwidthathalf
which we take to be the beamwidth at 250 µm. The esti-
maxima(FWHM)correspondingtotheHerschel beamsizes.
mate of central density then becomes a “beam-averaged”
valueoveraresolutionelementofareaπr2 .Foradistance The models involved central numberdensities of 105 cm−3,
min 106 cm−3, and 3×106 cm−3 with corresponding r values
of 140 pc, r corresponds to about 600 AU. 0
min
of 2500 AU, 4000 AU, and 1000 AU, respectively, and r
(ii) Most cores show some degree of asymmetry. This out
values of 1.3×104 AU, 1.7×104 AU, and 1.2×104 AU,
can degrade the quality of the global fit to a spherically-
symmetric model, causing the centre of symmetry to miss respectively. The corresponding core masses were 0.59 M⊙,
thephysicalcentreofthecore. Somenegativeconsequences 18.37 M⊙, and 3.11 M⊙, respectively. The synthesized im-
ages and corresponding Gaussian PSFs were then used as
includeanunderestimateofthecentraldensityandanover-
inputdata to theinversion algorithms. Theresults are pre-
estimate of the central temperature. To alleviate this, we
sented in Table 1.
estimatethe(x,y)location ofthecorecentreahead oftime
It is apparent that COREFIT gave masses and cen-
usingthepeakofacolumndensitymap,constructedatthe
tral temperatures in good agreement with the true model.
spatial resolution of the250 µm image. Themaximum like-
While COREFIT-PH reproduced the central temperatures
lihood estimation is then carried out using a 7-component
equallywell,itunderestimatedthemassesofthesesimulated
parameter vector which no longer involves the positional
coresbyfactorsof0.7,0.5,and0.5,respectively.Thereason
variables.
for these differences is that even though the two radiative
Having performed the position estimation and con- transfer codes (PHAETHON and MODUST) yield central
strained chi squared minimisation, the core mass is then temperaturesingoodagreementwitheachotherforagiven
set of model parameters, they produce divergent results for
the dust temperatures in the outer parts of the cores, due
3 Theinnerradiusofthisannulusistakenasthesizeofthesource largelytodifferencesindustmodelopacities.Sincetheouter
“footprint” which is estimated by getsources and includes all of partscomprise a greater fraction of themass than does the
the source emission on the observed images; the outer radius is central plateau region, this can lead to substantially dif-
set10%larger. ferent mass estimates given the same data. This problem
Properties of Starless and Prestellar Cores in Taurus 5
does not occur for COREFIT since the latter obtains the Evanset al. (2001) who considered various heating sources
temperature largely from the spectral variation of the data (theprimaryandsecondaryeffectsofcosmicraysandheat-
rather than from a physical model involving additional as- ing of dust grains by collisions with warmer gas particles)
sumptions. These calculations thus serve to illustrate the andconcludedthat heatingbytheISRFdominates overall
advantages of simultaneous estimation of theradial profiles othereffects.
of dust temperature and density. How do the COREFIT estimates of temperature and
mass compare with the preliminary values estimated from
the getsources SEDs? In the case of temperature, the rele-
5.2 Results obtained with observational data
vant comparison is between the SED-derived value and the
Table 2 shows the complete set of COREFIT parameter spatiallyaveragedCOREFITvalue;thedatainTable3then
estimates for each of the Taurus cores. Also included are give a mean “COREFIT minus SED” difference of -0.2 K,
the assumed values of the inner radius of the annulus used with a standard deviation of 1.1 for individual cores. The
forbackgroundestimation,equaltothegetsources footprint temperature estimates are thus consistent. With regard to
size. Table 3 shows a comparison of the mass and temper- mass,Fig.5showsthatSEDfittingundertheisothermalas-
ature estimates amongst the different techniques, which in- sumptionyieldsmassesthataresystematicallysmallerthan
cludeCOREFITandCOREFIT-PHaswell astheSEDfit- the COREFIT values; the mean ratio of COREFIT mass
tingdiscussedinSection3.Tofacilitatecomparisonbetween to SED-based mass is 1.5, with a standard deviation of 1.0
the COREFIT temperatures and the mean core tempera- in individualcases. Since theinternaltemperature gradient
tures estimated from the spatially integrated fluxesused in increaseswiththecoremass,onemightexpectthatthecor-
the SED fits, we include the spatially averaged COREFIT rection factor for SED-derived masses would increase with
temperature,T¯,definedasthedensity-weightedmeanvalue mass,althoughFig.5hastoomuchscattertoestablishthis.
of T(r) for r6r . The COREFIT-PH results include the Itmaybeevidentwhen theresultsareaveraged foramuch
out
values of the ISRF scaling factor, χ , the median value larger statistical sample of cores, although the correction
ISRF
of which is 0.33. The fact that this is noticeably less than may well depend on environmental factors such as the in-
unitycanprobablybeattributedtothefactthatthesecores tensity of the local ISRF.
are all embedded in filaments and hence the local ISRF is Fig. 6 shows a plot of estimated central temperature
attenuated by overlying filamentary material. As an exam- as a function of core mass. Linear regression indicates that
ple of the fitting results, Figs. 2 and 3 show the estimated these quantities are negatively correlated with a coefficient
density and temperature profiles for core No. 2 in Table 2, of -0.64. This correlation can be explained quite naturally
based on COREFIT and COREFIT-PH,respectively. as a consequence of increased shielding of the core, from
Fig. 4 shows that the two techniques yield consistent the ISRF, with increasing core mass. This being the case,
estimates of masses, but the radiative transfer calculations one would expect an even stronger correlation with peak
producecentral temperatures which are, on average, ∼2 K column density and this is confirmed by Fig. 7, for which
lowerthantheCOREFITestimates.Althoughthedifference theassociated correlation coefficient is -0.86.
isnotsignificantinindividualcases(thestandarddeviation Fig.8showsaplot ofαversusmass,whereαisthein-
being 1.4), it is clear from Fig. 4 that a systematic offset is dexofradialdensityvariationasdefinedbyEq.(2),andthe
present; the mean temperature difference, ∆T, is 1.9±0.3 masses aretheCOREFITvalues.Given therelatively large
K. uncertainties,theαvaluesare,forthemostpart,consistent
Basedontheresultsoftestingwithsyntheticdata,this with values expected for Bonnor-Ebert spheres, whereby
differenceseemstoo large tobeexplained bysystematic er- α = 2.5 provides an accurate empirical representation at
rorsassociated withdustgrain models, althoughwecannot radial distances up to the instability radius (Tafalla et al.
rule out that possibility. One could also question whether 2004), and that α decreases to its asymptotic value of 2
our χ values are spuriously low. We do, in fact, find beyondthat.
ISRF
that by forcing the latter parameter to a somewhat larger The general consistency with the Bonnor-Ebert model
value (0.5), the median ∆T can be reduced to zero with issupportedbythefactthatwhenthemaximumlikelihood
onlyamodest increase inthereducedchisquared,χ2 (0.85 fittingprocedureisrepeatedusingtheconstraintα=2,the
ν
as opposed to 0.83 for the best fit). The observations are chisquaredvaluesare,inmostcases,notsignificantlydiffer-
completely inconsistent with χ = 1.0, however. As an entfromthevaluesobtainedwhenαisallowedtovary.Two
ISRF
additional test, we can take the COREFIT estimate of the exceptions,however,arecores2and13,bothofwhicharefit
radial density distribution for each core and use the stan- significantlybetterbydensityprofilessteeperthanBonnor-
dalonePHAETHONcodetopredictthecentraltemperature Ebert(α=3.1and2.8,respectively),asillustratedbyFig.9
for any assumed value of χ . We thereby obtain con- fortheformercase.Specifically,thechisquared4 differences
ISRF
sistency with the COREFIT estimates with χ = 0.67. (17.2 and 7.5, respectively) translate into relative probabil-
ISRF
However,thisconsistencycomesatsignificant costinterms ities, for the “α=2” hypothesis, of ∼ 2×10−4 and 0.02,
of goodness of fit (the median χ2 increases to 2.27), and respectively. If confirmed, such behaviour may have some
ν
therefore does not serve to reconcile the COREFIT results important implications for core collapse models; a steepen-
withtheexpectationsofradiativetransfer.Insummary,the
COREFIT results are not entirely consistent with our as-
sumed model for dust heating by the ISRF, but further 4 To evaluate this quantity, the number of degrees of freedom,
workwill benecessarytodeterminewhetherthedifferences Ndf, was taken as the total number of resolution elements con-
are model-related or have astrophysical implications. So at tained within the fitted region for all five input images; Ndf is
this stage we haveno evidenceto contradict thefindings of then∼1700and∼1200forthetwocases,respectively.
6 K. A. Marsh et al.
Figure 2. Example of COREFIT results, for a 0.7 M⊙ core in Figure 3. COREFIT-PH results for the same core as inFig. 2.
L1495(No.2inTable2).Thesolidlinesindicatemaximumlikeli- Inthisvariantoftheestimationprocedure,thedusttemperature
hoodestimatesoftheprofilesofrelativevolumedensityanddust profileismodeledusingaradiativetransfercode(PHAETHON)
temperature. The dashed lines provide a measure of the uncer- insteadofestimatingitfromtheobservations.
taintyintheestimateddensityandtemperature.Theyrepresent
the results of a Monte Carlosimulation in which the estimation
procedure is repeated 10 times after adding synthetic measure-
mentnoisetotheobservedimages;thestandarddeviationofthe on this figure, for comparison, are theCOREFIT estimates
added noise corresponds to the estimated measurement noise of of those quantities. The seven points to the right of this
theobservedimages. curverepresent cores that we would consider to be gravita-
tionallyunstablebasedonthemodifiedBonnor-Ebertmod-
els. Although this is somewhat less than the 10 that were
ingofthedensitydistributionintheearlycollapsephaseis,
classified as unstable based on the SED fits, the difference
in fact, predicted by the model of Vorobyov& Basu (2005)
is probably not significant given that several points on the
in which thecollapsing corebegins todetach from itsouter
plot lie close to the“stability” line.
boundary.
The consistency between the above two procedures for
stability assessment is illustrated bythefact that theMBE
stability line in Fig. 10 provides a fairly clean demarcation
6 CORE STABILITY
between thecores classified as stable (open circles) and un-
Assessments of core stability are frequently made using stable (filled circles) from the simpler (SED-based) proce-
SED-based estimates of core mass and temperature and dure. These results therefore suggest that prestellar cores
observed source size, assuming that cores are isothermal canbeidentifiedreliably assuchusingrelatively simplecri-
and can be described as Bonnor-Ebert spheres (Lada et al. teria.
2008).Using the SED-based data in Table 3 in conjunction The Bonnor-Ebert model also provides a stability cri-
with the getsources estimates of core size, we thereby find terion with respect to the centre-to-edge density contrast,
thattheestimatedcoremassexceedstheBonnor-Ebertcrit- whereby values greater than 14 indicate instability to
ical mass for 10 of our 20 cores, suggesting that half of our gravitational collapse, both for the isothermal and non-
cores are unstableto gravitational collapse. isothermalcases(Sipil¨a, Harju & Juvela2011).Howeverthe
OurCOREFITparameterestimatesenableustomake outerboundariesarenotwelldefinedforthepresentsample
amoredetailedassessmentofcorestabilitybasedonacom- of cores, and consequently the contrast values are uncer-
parison with the results of hydrostatic model calculations taininmost cases.Twoexceptionsarecores2and13, both
thattakeaccountofthenon-isothermalnatureofthecores. ofwhichhavecontrast estimateswhose significanceexceeds
This is facilitated by the modified Bonnor-Ebert (MBE) 3σ. In both cases the mass exceeds the Bonnor-Ebert crit-
sphere models of Sipil¨a, Harju & Juvela (2011). Adopting ical mass (by ratios of 1.2 and 6.0, respectively), and the
their model curves, based on theLi & Draine(2001) grains centre-to-edgecontrast values(20±6and 104±32, respec-
which best reproduce our estimated core temperatures, the tively) are in excess of 14. So for those two cores, at least,
locus of critical non-isothermal models on a density versus thecorestabilitydeducedfromthedensityconstrastisthus
massplotisshownbythesolidlineonFig.10.Alsoplotted consistent with that assessed from total mass.
Properties of Starless and Prestellar Cores in Taurus 7
Table 1.Resultsoftestingwithsynthetic data.
T0 [K] Mass[M⊙] PeakH2 col.dens.[1022 cm−2]
a b
Model Std. Alt. True Std. Alt. True Std. Alt. True
1 10.1 8.6 10.0 0.61 0.39 0.59 0.59 0.45 1.04
2 6.8 6.5 6.5 22.7 9.48 18.4 23.9 5.65 16.1
3 7.8 6.5 6.7 3.30 1.46 3.11 7.95 4.91 13.4
a
StandardversionofCOREFIT
b
Alternateversion(COREFIT-PH)
Table 2.COREFITparameterestimates forthe20Tauruscores.
Core RA Dec rannulusa r0 rout n0 αb T0c T1 T2d
No. (J2000) (J2000) [103 AU] [103 AU] [103 AU] [105 cm−3] [K] [K] [K]
1 04:13:35.8 +28:21:11 7.56 3.5±1.2 7.1±0.2 0.5±0.1 2.0±0.6 9.5±0.5 11.2±0.1 −1.4±0.6
2 04:17:00.6 +28:26:32 16.38 4.7±0.2 13.2±0.6 0.7±0.1 3.1±0.4 10.7±0.3 12.5±0.2 −1.2±0.2
3 04:17:32.3 +27:41:27 11.20 3.5±3.1 7.3±0.4 0.2±0.1 2.0±1.0 12.3±0.8 13.1±1.2 0.2±0.1
4 04:17:35.2 +28:06:36 10.30 0.6±0.2 8.4±0.4 9.9±2.9 3.7±0.2 7.1±0.6 23.7±1.2 −2.6±0.5
5 04:17:36.2 +27:55:46 13.20 2.9±1.0 11.8±0.4 0.8±0.3 2.6±0.4 9.4±0.4 12.0±0.3 −2.3±0.5
6 04:17:41.8 +28:08:47 10.08 0.8±0.2 8.8±1.2 26±18 2.0±0.4 7.0±0.1 8.3±0.4 −1.1±0.3
7 04:17:43.2 +28:05:59 7.14 1.0±0.4 6.9±0.2 13±6 2.6±0.3 7.1±0.4 10.1±0.2 −2.9±0.5
8 04:17:49.4 +27:50:13 8.10 2.9±2.9 7.7±0.2 0.5±0.2 1.9±1.8 9.9±1.6 10.8±0.5 0.9±0.6
9 04:17:50.6 +27:56:01 13.86 4.5±0.2 10.4±0.4 1.9±0.1 3.4±0.6 8.0±0.2 10.1±0.2 −1.0±0.2
10 04:17:52.0 +28:12:26 12.60 4.3±1.7 11.2±0.2 0.9±0.4 2.2±0.6 10.0±0.6 9.7±0.6 −0.1±0.3
11 04:17:52.5 +28:23:43 12.15 2.1±1.0 9.5±0.2 1.0±0.3 1.9±0.4 9.8±0.6 11.2±0.3 −0.4±0.2
12 04:18:03.8 +28:23:06 8.75 2.3±0.6 8.6±0.2 2.3±0.4 3.0±0.9 9.9±1.1 10.8±1.1 0.9±0.7
13 04:18:08.4 +28:05:12 13.86 2.3±0.8 13.4±0.2 6.8±1.8 2.8±0.4 6.0±0.5 11.4±0.3 −3.2±0.5
14 04:18:11.5 +27:35:15 7.45 2.3±1.4 7.3±0.2 1.9±0.5 2.0±0.5 7.8±0.4 10.1±0.3 −2.2±0.7
15 04:19:37.6 +27:15:31 11.76 2.7±0.6 10.7±0.4 1.6±0.4 2.0±0.2 8.8±0.4 10.6±0.1 −1.5±0.2
16 04:19:51.7 +27:11:33 9.24 3.1±0.4 8.9±0.2 3.9±0.5 3.4±0.7 6.4±0.2 9.6±0.3 −3.0±0.5
17 04:20:02.9 +28:12:26 10.30 1.4±0.4 10.0±0.4 0.5±0.3 2.0±0.3 10.7±0.4 12.7±0.2 −1.9±0.5
18 04:20:52.5 +27:02:20 5.30 5.2±2.9 5.2±0.2 0.3±0.1 indet. 11.4±0.9 11.3±0.4 0.1±0.4
19 04:21:06.8 +26:57:45 8.10 2.7±1.2 4.7±0.6 0.6±0.2 3.0±1.2 11.1±0.6 11.8±0.2 0.1±0.0
20 04:21:12.0 +26:55:51 8.75 2.9±0.8 8.6±0.2 0.3±0.1 4.0±1.2 10.1±0.7 13.9±0.1 −1.6±0.6
a
Innerradiusoftheannulususedforbackground estimation.
b Anentryof‘indet.’indicatesthatαisindeterminatefromthedata; thisoccursifr0≃rout.
c Centralcoretemperature,effectively anaverageoveraresolutionelementofradiusrmin=600AU.
d NegativevaluesofT2 indicatenegativecurvatureofthetemperatureprofileandhavenocorrespondencewithactualtemperatures.
7 COMPARISON WITH PREVIOUS (20′′) or the Herschel data (18′′ at 250 µm). These off-
OBSERVATIONS setsaresomewhatsurprising,sincepreviouscomparisonsbe-
tweenH13CO+ anddustcontinuummapshaveshowngood
The deduced physical properties of our cores may be
correspondence (Umemoto et al. 2002). Onecould question
compared with previously published spectral line data in
whethertheyareduetogriddingerrorsintheH13CO+data,
H13CO+ and N H+, both of which are known to be good
2 inviewofthefactthattheobservationsweremadeonarel-
tracers of high density gas (n(H2) ∼> 105 cm−3). Of our 20 ativelycoarsegrid(theeightcoresofOnishi et al.(2002)in
cores,wefindaccompanyingobservationsfor10inH13CO+ Table4aresplitevenlybetween30′′ and60′′ gridspacings).
(Onishiet al.2002)andseveninN H+ (Hacar et al.2013).
2 However,themeasuredoffsets shownocorrelation with the
The relevant parameters are given in Table 4. gridspacing—themeanoffsetisapproximately50′′ ineither
Considering first the H13CO+ data, comparison of ob-
case; this argues against gridding error as an explanation.
servedpeak locations with dustcontinuumsourcepositions
Themost likely reason for thesystematic offsetsis that the
fromCOREFITshowsadistinctlackofdetailedcorrespon-
H13CO+ is frozen out at the low (∼< 10 K) temperatures of
dence. This behaviour is apparent in Fig. 1 and from Ta-
thecore centres (Walmsley et al. 2004).
ble 4 which includes the angular distance (labeled as “Off-
set” in the table) between each of the H13CO+ source lo- Detailed comparison of the dust continuum core loca-
cations and the corresponding dust continuum core loca- tions with the H13CO+ maps (four examples of which are
tion. The median distance is 59′′, considerably larger than giveninFig.10)showsthatthemajorityofsourcesareelon-
the spatial resolution of either the H13CO+ observations gated and/or double and that in some cases (Onishi core
8 K. A. Marsh et al.
Table 3.Comparisonofmassesandtemperatures estimated usingthe threedifferenttechniques discussed
inthetext
a
SED-fitting COREFIT COREFIT-PH
Core Mass T Mass T0 T¯b Mass T0 χISRFc
No. [M⊙] [K] [M⊙] [K] [K] [M⊙] [K]
1 1.19±0.05 9.9±0.3 0.20±0.01 9.5±0.5 10.8 0.25 8.2 0.28
2 0.71±0.04 11.8±0.5 0.84±0.04 10.7±0.3 11.8 0.72 8.4 0.90
3 0.10±0.01 12.3±0.5 0.09±0.04 12.3±0.8 12.7 0.23 9.1 0.37
4 0.05±0.01 12.6±0.8 0.04±0.01 7.1±0.6 9.3 0.08 9.1 0.29
5 0.20±0.01 11.3±0.1 0.37±0.02 9.4±0.4 10.9 0.32 8.0 0.37
6 1.01±0.15 8.0±0.6 1.70±0.34 7.0±0.1 7.7 1.64 5.0 0.26
7 0.22±0.10 8.8±1.1 0.49±0.09 7.1±0.4 8.6 0.37 6.0 0.31
8 0.07±0.01 9.9±1.5 0.19±0.04 9.9±1.6 10.3 0.25 6.7 0.14
9 1.53±0.02 9.2±0.1 1.44±0.09 8.0±0.2 9.2 1.53 5.5 0.39
10 1.30±0.20 8.8±0.9 0.96±0.02 10.0±0.6 9.9 1.35 5.8 0.32
11 0.20±0.03 11.8±1.1 0.32±0.06 9.8±0.6 10.6 0.41 7.4 0.29
12 0.42±0.05 9.2±0.6 0.41±0.06 9.9±1.1 10.1 0.40 6.6 0.39
13 1.60±0.28 8.8±1.0 2.03±0.16 6.0±0.5 8.3 2.21 5.4 0.32
14 0.47±0.11 8.8±1.7 0.46±0.05 7.8±0.4 9.4 0.33 6.7 0.25
15 0.21±0.07 11.2±1.9 0.84±0.08 8.8±0.4 10.0 1.04 6.1 0.36
16 0.36±0.06 8.7±0.5 1.08±0.12 6.4±0.2 8.3 1.52 5.0 0.26
17 0.05±0.01 12.5±1.2 0.08±0.01 10.7±0.4 11.9 0.12 8.8 0.18
18 0.21±0.03 9.6±0.8 0.09±0.02 11.4±0.9 11.3 0.07 9.2 0.25
19 0.08±0.01 11.8±0.8 0.08±0.02 11.1±0.6 11.5 0.09 8.6 0.38
20 0.02±0.01 13.6±0.7 0.06±0.01 10.1±0.7 11.8 0.05 10.2 0.28
a
Basedonspatiallyintegratedfluxes.
b Density-weightedmeanvalueofT(r)forr6rout.
c
EstimatedISRFscalingfactor.
Table 4.Comparisonwithpreviouslypublishedspectrallinedata.
Corea IDb Offsetc [arcsec] Radius[pc] Mass[M⊙]d n(H2)[105 cm−3]
No. Onishi Hacar H13CO+ N2H+ Duste H13CO+ N2H+ Dust H13CO+ Dust H13CO+
1 3 ... 41 ... 0.034 0.021 ... 0.2 1.7 0.5 0.9
4 5 ... 74 ... 0.041 0.054 ... 0.04 6.5 9.8 1.9
6 5 1 93 43 0.043 0.054 0.048 1.7 6.5 25 1.9
7 5 ... 91 ... 0.034 0.054 ... 0.5 6.5 13 1.9
9 ... 2 ... 8.4 0.050 ... 0.027 1.4 ... 1.9 ...
10 6 ... 52 ... 0.054 0.034 0.051 1.0 5.8 0.9 1.2
12 7 5 82 31 0.042 0.035 0.030 0.4 2.9 2.3 1.9
13 8 6 24 44 0.065 0.064 0.053 2.0 5.0 6.8 1.0
14 9 7 44 21 0.035 0.060 ... 0.5 4.2 1.9 1.0
15 13a 10 8.0 19 0.052 0.048 0.047 0.8 3.4 1.6 1.4
16 ... 12 ... 9.4 0.043 ... 0.034 1.1 ... 3.9 ...
18 16a ... 59 ... 0.025 0.028 ... 0.09 3.0 0.3 2.5
a
AslistedinTable2.
b Objectnumberinpreviouslypublishedsourcelists:Onishietal.(2002)inH13CO+,andHacaretal.(2013)inN2H+.
c
AngularoffsetfromtheCOREFIT(dustcontinuum)position.
d
Themassquotedinthe“Dust”columnrepresentstheCOREFITestimateoftotalmass(gas+dust)basedonthedustthermal
continuum inthe70–500µmrange;themassquotedforH13CO+ representsavirialmassderivedbyOnishietal.(2002).
e Theradiusquotedhereisrout fromTable2,converted topc.
No.3inparticular)thedustcontinuumsourcefallsbetween imagesandtheir250µmcounterpartsshowthat,ingeneral,
thepairofH13CO+ components.Inothercases(e.g.Onishi theelongationandsourcealignmentinH13CO+isalongthe
core No. 16a), the dust continuum peak falls on a nearby filament,sowehavearod-like,ratherthanspherical,geom-
secondary maximum of the H13CO+ emission. In the latter etry. The picture which thus emerges is that when a core
case, surprisingly,themain peak of H13CO+ falls in a local formsinafilament(Andr´eet al.2010),weseethecorecen-
minimum of dust emission. Comparisons between H13CO+ tre in dust continuum emission and the warmer (but still
Properties of Starless and Prestellar Cores in Taurus 9
Figure 5. SED-derived mass based on isothermal assumption
versus the mass from COREFIT model. For reference, the solid
linerepresentsthelocusofequalmasses.
Figure 4. Comparison between parameter estimates, obtained
using COREFIT and COREFIT-PH, for the 20 selected cores.
In the former procedure, the dust temperature profile is esti-
mateddirectlyfromtheobservations,whileinthelatteritismod-
eledusingradiativetransfer.Upper plot:COREFITmassversus
COREFIT-PH mass. For reference, the solid line represents the
locus of equal masses. Lower plot: ∆T versus mass, where ∆T
represents the difference in estimated temperature (COREFIT
minusCOREFIT-PH).
dense, ∼ 105 cm−3) H13CO+ gas on either side of it in a
dumbbell-like configuration. The median separation of the
dust continuum and H13CO+ sources then corresponds to
thetypicalradius of thedepletion zone. Foran ensemble of Figure 6. Central dust temperature, T0, as a function of core
randomlyorientedfilaments,themeanprojectedseparation mass.
isπ/4timestheactualseparation,whichmeansthatoures-
timated median separation of 59′′ corresponds to an actual
separation of 75′′, or about 1.1×104 AU at the distance
of L1495. This is similar to the radius of the dark-cloud
chemistry zone in which carbon-bearing molecules become
gaseous (Caselli 2011).
Comparing the estimated masses, Table 4 shows that
thevaluesestimated fromdustcontinuumobservationsare,
in most cases, much smaller than those based on H13CO+.
Thediscrepancyrangesfromafactorof∼2tomorethanan
order of magnitude. Based on the mass and positional dis-
crepancies it is clear that H13CO+ and submillimetre con-
tinuum are not mapping thesame structures. Nevertheless,
it remains to explain why so much of the expected dust
emission from the H13CO+ emitting gas is apparently not
being seen in the submillimetre continuum. It is unlikely
to be a result of the background subtraction in COREFIT
since the COREFIT mass estimates match the SED-based
values from getsources fluxes within ∼ 30% and the only
Figure 7. Central dust temperature, T0, as a function of peak
background that was subtracted during the latter process- columndensityofH2 molecules.
ingcorresponded to thenaturalspatial scale of thebroader
underlyingemission structure.
10 K. A. Marsh et al.
Figure 8. The estimated index of radial density falloff, α, as a Figure10.CentralnumberdensityofH2moleculesasafunction
functionofcoremass. of core mass. The circles represent the COREFIT estimates for
L1495;filledsymbolsdesignatethesubsetofcoreswhoseprelimi-
naryassessmentofdynamicalstatussuggeststhattheyaregravi-
tationallybound,basedongetsourcesfluxesandsizesinconjunc-
tionwiththestandardmodelofisothermalBonnor-Ebertspheres.
For comparison, the solid line represents the locus of critically-
stablenon-isothermalBonnor-Ebertspheres(Sipil¨a,Harju&Ju-
vela(2011); points totherightofthislinerepresentcores which
areunstabletogravitational collapseaccordingtothatmodel.
Figure 9. Radial profiles of the images of core No. 2 at four
wavelengths, showingthe matchbetween observations andmod-
els for two different values of the radial density index, α. Solid
line: observed profile; dashed line: best fitting model (α = 3.1)
convolvedwiththecorrespondingPSFateachwavelength); dot-
ted line: same, except for the constraint α=2.0. Note that the
lattermodelresultsinapoorfitinthecentralregion.
The most likely explanation for the discrepancy is an
overestimation ofthevirialmassofthegascomponentdue,
inpart,totheassumptionbyOnishi et al.(2002)ofuniform
velocity dispersion. Specifically, the velocity dispersion of Figure 11. Examples of dust continuum core locations in rela-
therelativelycoolgasbeingprobedbydustemissionislikely tion to H13CO+ emission. The estimated locations of cores 1,
tobeatleastafactoroftwolowerthanthatofH13CO+,as 13, 14 and 15 (corresponding to Onishi core Nos. 3, 8, 9, and
suggested by theN H+ observations of Hacar et al. (2013), 13a, respectively) are superposed on H13CO+ maps taken from
2
Onishietal. (2002) (B1950 coordinates). In each case, the loca-
and since the estimated virial mass depends on the square
tionofpeakdustcolumndensityisindicatedbyaredcross.The
of that dispersion, it could have been overestimated by a
greencrossinOnishifield(9)representsasecondarypeakofdust
factor of up to 4. Two additional effects, both of which are
emission.TheblackcrossinOnishifield(13)representsaproto-
likely tohave led to overestimation of the virial mass are: starlocation.
(i) the Onishi et al. (2002) virial mass was based on as-
sumedspherical shapeas opposed tothefilamentary geom-
etryobserved,andhencethesourcevolumesmayhavebeen
overestimated;